Find the number of molecules in 1 cm3 of an ideal gas at 0°C and at a pressure of 10–5 mm of mercury.

Given


Volume of ideal gas V=1cm3


1cm=m


V=m3


Temperature of ideal gas=0


T(K)=T ()+273.15


T=T(K)=0+273.15=273.15K


Pressure of ideal gas P=mm of Hg


1mm of Hg= 133.32Pa


P=mm of Hg=133.32Pa


We know ideal gas equation


PV=nRT


Where V= volume of gas


R=gas constant=8.31J/molK


T=temperature


n=number of moles of gas


P=pressure of gas.


So,





Number of molecules = Avogadro numbernumber of moles


Number of molecules=n


=


=3.538


Therefore,


Number of molecules in 1 cm3 of an ideal gas at 0°C and at a pressure of 10–5 mm of mercury is 3.538.


1